Department of Electrical and Computer Engineering - University of New Brunswick, Fredericton, NB, Canada
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EE4253 Digital Communications
Department of Electrical and Computer Engineering - University of New Brunswick, Fredericton, NB, Canada |
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Shift registers with feedback essentially divide polynomials to create distinctive binary sequences.
This online tool draws and analyzes digital circuits which generate Linear Recursive Sequences (LRS) based on a defining polynomial P(x). The circuit shown below is traced through all possible states. Maximum length sequences are identified. The autocorrelation of each sequence can also be checked (maximum 1023 bits).
alternate configuration
Circuit based on P(x) = x4+x3+x2+x+1
| Sequence #1 (Starting with 0) |
| States: 0 ⇒ 0, forever... |
| Sequence #2 (Starting with 1) |
| States: 1 ⇒ 8 ⇒ 12 ⇒ 6 ⇒ 3 ⇒ 1 |
| Period = 5 (autocorrelation)
Output = 10001... |
| Sequence #3 (Starting with 2) |
| States: 2 ⇒ 9 ⇒ 4 ⇒ 10 ⇒ 5 ⇒ 2 |
| Period = 5 (autocorrelation)
Output = 01001... |
| Sequence #4 (Starting with 7) |
| States: 7 ⇒ 11 ⇒ 13 ⇒ 14 ⇒ 15 ⇒ 7 |
| Period = 5 (autocorrelation)
Output = 11101... |
In this example, a prime polynomial failed to give a maximum length sequence. For this polynomial of degree 4, the maximum length sequence would have a period of 24-1 states. Use of a prime polynomial is a necessary but not sufficient condition for a maximum length sequence. Only "primitive primes" give maximum length sequences. |
| Modulo 2 addition is shown schematically equivalent to Exclusive-OR gates. | 
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Thu May 23 12:15:38 ADT 2013
Last Updated: 28 NOV 98 |
Richard Tervo [ tervo@unb.ca ] | Back to the course homepage... |
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